We study the two-dimensional system of Time-Dependent Ginzburg-Landau Equations (TDGL) for modeling a thin film of superconductor subject to a uniform magnetic field. We discretize the TDGL for the space variables using bond variables and staggered grid partitioning technique. By investigating the temporal evolution of semi-discrete Helmholtz enery functional and that of Semi-discretized TDGL, we provide bounds for some observable physical quantities of interest such as superelectron density, supercurrent density, charge density, electric field, and induced magnetic field.
COŞKUN, ERHAN (1997) "On some Bounds for the Solutions of the Semi-Discretized Time-Dependent Ginzburg-Landau Equations," Turkish Journal of Mathematics: Vol. 21: No. 5, Article 3. Available at: https://journals.tubitak.gov.tr/math/vol21/iss5/3